What's the highest 'order' data structure

Not sure exactly how to define this but here's the basis of the question (very loosely)

• All lists can be contained in tree's

• all trees can be contained in a graph

• all graphs can be contained in a multi graph,

• and all multigraphs can be contained in a hypergraph (never actually heard of a hypergraph before searching for an answer to this, so may not have it quite right)

So there's a containment hierarchy of 'complexity' of data structures. Is Hypergraph the highest one, is there a proof of this, and is there a name for the study of whatever this is.

By highest one, I mean all structures can be represented as a hypergraph if I chose to. So in any code I could represent all the structures by using a number of hypergraphs (not that I would). tia

[Update] Perhaps an alternative way to ask it is, for any arrangement of data structures consisting of nodes and edges. Does there exist a structure that can't be contained in a hypergraph.

Then there is a second question - is there any data structure which can't be represented using nodes and edges.

Perhaps this is an interesting question with explicit answers, but you probably really have a problem with "exactly how to define this".

A list does not directly corresponds to a unique data structure, nor does a tree. A singly linked list corresponds to a (sufficiently unique) data structure, as does a binary tree. When you say multi graph, you probably want to refer to a quiver, i.e. a directed multigraph (edges with own identity). A binary or ternary quiver would again correspond to a (sufficiently unique) data structure.

However, any sufficiently canonical (and efficient) realization of a (n-ary) quiver as a data structure would probably not match well with the way datatypes are handled in "common" programming languages, where the size of an object with a certain datatype shouldn't depend on the actual content of that object. Therefore, this would be the point at which I would stop to look for a higher order data structure (than a quiver, looking for function like data structures and continuations certainly is useful). My reason for this is that I don't see the practical usefulness of a higher order data structure if it cannot be realized efficiently within "common" programming languages.

StackExchange Computer Science Q#4760, answer score: 3